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UI STAT 4520 - Project Report

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Bayesian analysis for heart rate variability in Hypoplastic Left HeartSyndrome infants22S:138 Project ReportDivya KudvaIntroductionHypoplastic Left Heart Syndrome (HLHS)Hypoplastic left heart syndrome is a congenital heart disorder that refers to the underdevelopment of cardiac structures on the left side of the heart. HLHS accounts for 7- 9% of all the congenital heart defects occurring in children (1). It occurs in every 1-4 per 10000 live births (2) and in United States alone there are over 1000 cases of HLHS each year (3). One of the treatment options for HLHS is staged cardiac palliation which consists of three surgeries that are performed at different times during the infant’s life. Norwood’s surgery is the first operation which is typically performed within the first 2 weeks of life. Norwood’s is a high risk procedure with a mortality rate of up to 30 %. Causes of mortality following Norwood are largely unknown as most of the infants die suddenly from cardiac failure.We (the research group I work with) are interested in determining the cause of sudden death in HLHS infants. We believe that an imbalance in the cardiac autonomic tone is responsible for the sudden death of these infants. Our aim is to determine whether the imbalance in autonomic tone is persistent at birth or whether Norwood’s surgery is responsible for the disruption of tone. Heart Rate Variability analysis is used in order to assess the cardiac autonomic function.Heart Rate Variability (HRV)The heart does not beat at a constant rate but displays periodic variations over time. This beat-to-beat alteration in heart rate or the difference between the R-R peaks in the QRS complex of the ECG signal is known as heart rate variability (Figure 1). The normal variability in heart rate is due to the synergistic action of the two branches of the 1autonomic nervous system i.e. the sympathetic and parasympathetic nervous system. Reduced HRV indicates reduction in the variations in the heart rate which may indicate failure of certain regulatory mechanisms in the body.Figure 1: The variations in the R-R intervals (HRV) indicating HRV is a measure of the beat-to-beat changes in heart rate (4).Depressed HRV is often a cause of concern because it is associated with an increased risk of mortality. Reduced HRV has been observed in adults during myocardial infraction, diabetic neuropathy, cardiac transplantation, etc. (5-7). In infants and neonates reduced HRV has been reported in conditions such as respiratory distress syndrome (RDS), reduced gestational age, and congenital cardiac abnormalities (8-10).HypothesisOne of the objectives in this research study is to determine whether there is a difference in the HRV (i.e. difference in the autonomic function) in the HLHS infants as compared to the age matched normal infant population before cardiac surgery. Our hypothesis is that HRV in HLHS infants will be diminished as compared to the normal infants i.e. the variations in HRV within the hypoplast group will be reduced as comparedto the control group.2Infant populationFor this study, the infant population was divided into two groups. Group I consisted of five normal newborn healthy infants. Group II consisted of five infants diagnosed with HLHS. The electrocardiograph data was recorded using Zymed Philips Digitrak Plus 24-hour Holter monitor. A Holter monitor is a portable device that continuously measures the electrical activity of the heart using electrodes that are attached to the skin. After the collection of Holter data, Philips software was used to determine the exact time of occurrence of the R peak in the QRS complex of the ECG signal. The difference between the R-R peaks was computed and stored which is essentially the HRV data.DatasetFor this Bayesian analysis project, I am using HRV data for HLHS infants and their age matched normal controls prior to cardiac surgery. Twenty 5-minute segments of heartbeat data are selected for each infant and the mean HRV for each of the 5-minute segments is computed. Thus, the dataset consists of 20 HRV values for each infant in Group I and II.MethodBayesian ModelA hierarchical model was implemented with the HRV data considered to be normally distributed, yij = Normal (mean[i], precwithin)where yij is the HRV for the ith subject and jth sample mean [i] is the mean HRV for the ith subject over the entire time duration precwithin is the precision (inverse of variance) within the subjectThe mean HRV for each subject, mean[i] is considered to be normally distributed, mean [i] = Normal (theta, precbetween)where theta is the mean HRV for all the subjects theta ~ Normal(mu, variance)3precbetween is the precision (inverse of variance) between the subjectsThe bayesian model was implemented in WINBUGS with different initial values and priors for Group I and II.Prior selectionI did not have any prior information that would help me determine the priors for the model. I therefore selected the priors based on my knowledge of HRV values in normal and diseased states. Inverse gamma priors were selected for the precision betweensubjects, precbetween and for precision within subjects, precwithin. Different priors were selected for Group I and II for the within subject precision. For an inverse gamma distribution,θ ~ Inv-gamma (α, β)mean = , 11ba >a - (1)variance = 22, 2( 1) ( 1)ba >a - a - (2)1. precwithin1 for Group I:mean = 700variance = 10,000Solving for (1) and (2)α = 51 and β = 350002. precwithin2 for Group II:mean = 300variance = 5000Solving for (1) and (2)α = 20 and β = 570043. precbetween for Group I and II:mean = 500variance = 10,000Solving for (1) and (2)α = 27 and β = 13000Bayesian analysisThree parallel Markov chains of 10,000 iterations were run with different initial values for theta, precbetween, precwithin. The first 1000 samples from each chain were discarded as burn-in. The ratio of the variance in HRV within Group I infants, varwithin1 to the variance in HRV in Group II infants, varwithin2 was computed. For both groups I and II, the parameters monitored were theta, varwithin, varbetween, and ratio. The aim was to monitorthe variation in HRV within each group and the 95% confidence interval for ratio in orderto determine whether there was a difference in HRV in the two groups.ResultsConvergenceIn order to assess the convergence of the model,


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